Mathematics · Statistics

JEE Main 2025 — 2 April, Evening Shift — Question 27

If the mean and the variance of $6,4, a, 8, b, 12,10$ , 13 are 9 and 9.25 respectively, then $a+b+a b$ is equal

to :

Answer: A

Mean $=\frac{6+4+a+8+b+12+10+13}{8}=9$

$53+a+b+=72$

$\Rightarrow a+b=19$ and

And $\frac{36+16+a^{2}+64+b^{2}+144+100+169}{8}-9^{2}=9.25$

$\Rightarrow \frac{529+a^{2}+b^{2}}{8}=90.25$

$\Rightarrow a^{2}+b^{2}=193$

$\therefore \quad a=7, b=12$

Hence, $a+b+a b=19+84=103$

Answer key and solution verified before publishing.

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